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Abstract

A method for generating smooth freeform optical surfaces from B-spline is proposed. In this method, the unit tangent vectors of feature data points are employed as constraints. Based on design methods of freeform surface, both feature data points and unit tangent vectors are obtained, and control points and knot vectors of the freeform surface are computed by the interpolation theory. The freeform surfaces are constructed with the control points and knot vectors to ensure the desired normal at each feature data point. Freeform surfaces are constructed by this method and compared with the traditional method. The results show that beams are controlled well by this method with a maximum uniformity more than 99%, and better results can be obtained with fewer feature data points for this method.

References

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Table 4

ad denotes distance between the front surface of the freeform lens and the target plane; L and W are length and width of the freeform surface; Dx and Dy are length and width of the illumination zone, and (X, Y) are coordinates of the central point M of the illumination zone, see Fig. 10.

Table 5

Comparison of Irradiance Uniformities for the Two Construction Methods

Number of data points

6

7

8

9

10

15

20

25

30

Uniformity

Utv

90.10%

93.63%

96.12%

97.31%

98.11%

99.00%

99.06%

99.04%

99.01%

Tcm

89.49%

90.24%

88.01%

88.02%

94.62%

93.26%

91.72%

92.39%

88.20%

Tables (5)

Table 1

Design Parameters for Annular Illumination

φmax

R

n

z0

Rmin

Rmax

45°

10mm

1.4935

30mm

30mm

70mm

Table 2

Comparison of Irradiance Uniformities for the Two Construction Methods

Table 4

ad denotes distance between the front surface of the freeform lens and the target plane; L and W are length and width of the freeform surface; Dx and Dy are length and width of the illumination zone, and (X, Y) are coordinates of the central point M of the illumination zone, see Fig. 10.

Table 5

Comparison of Irradiance Uniformities for the Two Construction Methods